Variance of vector fields -- Definition and properties
Abstract
We give a self contained presentation of the notion of variance of a vector field introduced by Jean Ecalle and Bruno Vallet in ev following a previous work of Jean Ecalle and Dana Schlomiuk in es. We give complete proofs and definitions of various results stated in these articles. Following J. Ecalle and D. Schlomiuk, We illustrate the interest of the variance by giving a complete proof of the formulas for the mould defining the nilpotent part of a resonant vector field.
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